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August, 1978 Type, Cotype and Levy Measures in Banach Spaces
Aloisio Araujo, Evarist Gine M.
Ann. Probab. 6(4): 637-643 (August, 1978). DOI: 10.1214/aop/1176995483


A characterization of type $p$ and cotype $p$ separable Banach spaces is given in terms of integrability properties of Levy measures. The following consequences are derived: (i) a separable Banach space is isomorphic to Hilbert space if and only if the set of Levy measures on it coincides with the set of Borel measures which integrate the function $\min (1, \|x\|^2)$; and (ii) the classical Levy-Khintchine representation of characteristic functions of infinitely divisible distributions holds in separable Banach spaces of cotype 2, in particular, in the separable $L_p$ spaces for $p \in \lbrack 1,2\rbrack$.


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Aloisio Araujo. Evarist Gine M.. "Type, Cotype and Levy Measures in Banach Spaces." Ann. Probab. 6 (4) 637 - 643, August, 1978.


Published: August, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0384.60003
MathSciNet: MR482910
Digital Object Identifier: 10.1214/aop/1176995483

Primary: 60B05
Secondary: 60E05

Keywords: Levy measures , the Levy-Khintchine representation , type and cotype 2 spaces

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 4 • August, 1978
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